#### mnnn

##### New member
please find the mathematical problem below:

man and woman buy property together for £275k

man puts down a deposit of his own money of £40k, agreed that when the property is sold £40k is to be paid back to the man, and any profit thereafter to be split 50/50

the mortgage is £235k (capital only mortgage so it does not reduce over time)
equity in the property at point of sale is £40k

woman later lends man £75k, agreed that when the property is sold, (as long as it sells for a profit) the man will pay her back from the equity. any profit above that is split 50/50

years later the property sells for £325k

who owes who what and why?

#### Jomo

##### Elite Member
Please show us your attempt at this problem and where you are stuck. We have no idea how to help you unless we see the way you want to attack this problem. So please follow our guidelines and post back showing us your work.

#### mnnn

##### New member
hi jomo , thank you for your prompt response.

my attempt is

that the man and the woman each walk away with £7.5k each after the sale of £325k

Please could you confirm if this is correct?

#### Subhotosh Khan

##### Super Moderator
Staff member
hi jomo , thank you for your prompt response.

my attempt is

that the man and the woman each walk away with £7.5k each after the sale of £325k

Please could you confirm if this is correct?

Please explain the process by which you arrived at those numbers.

#### mnnn

##### New member
325k (sale price) minus 235k (the mortgage)

= 90k equity

40k from this sale is owed to the man but thereafter 70k of this sale is owed to the woman.

this leaves a profit of 20k to be split equally between both parties.

please confirm if that is correct?

#### Jomo

##### Elite Member
There is 90k in equity.
The first 40k goes back to the man.
This leaves 50k left over.
The man gets 25k and the woman gets 25k.

So the man gets 40k+25k = 65k and the woman gets 25k. This seems correct as 65k + 25k = 90k.

Now the man still owes the woman $70k. So the woman needs to get back 25k + 70k = 95k. This means that all 90k from the equity goes to the woman and the man still owes the woman 5k You just can't take the 70k out of the pot and give it to the woman as half of that money was hers anyways! Do you see that? There is no reason, as I detailed above, to involve the 70k loan in the transaction for the house. It had nothing to do with the house other than the promise to pay it back after the house was sold. On the other hand that initial downpayment from the man had everything to do with the house. If you prefer you can think of the man loaning the woman 20k (so now they each put down 20k each on the house) and again this 20k loan to the woman has nothing to do with the house. If you consider both loans independent with the purchase of the house, then the man loaned the woman 20k and the woman loaned the man 70k so in the end the woman loaned the man 50k. After the sale of the house they each get back 45k. Then the man needs to pay the woman the 50k loan back. Last edited: #### Jomo ##### Elite Member hi jomo , thank you for your prompt response. my attempt is that the man and the woman each walk away with £7.5k each after the sale of £325k Please could you confirm if this is correct? I just have one question for you? The banks hands the woman and man a total of 90k. The woman takes 7.5k and the man takes 7.5k. That is a total of 15k. WHERE IS THE OTHER 75k and can I please have it? Do you understand that however the money is split up, even if incorrectly, the sum of the money that the man and woman gets must total 90k! Otherwise where is the rest of the money???? #### JeffM ##### Elite Member The problem is almost insanely worded, at least as you have paraphrased it. Please give the exact and complete wording of the problem. Perhaps it was not written by a chimpanzee. Purchase price = 275. Sales price = 325. Is that correct? Net gain = profit = 325 - 275 = 50. Proceeds from the transaction are obviously 325, and profit on the transaction is just as obviously 50. Now what do the almost incoherent words "when the property is sold, (as long as it sells for a profit) the man will pay her back from the equity. any profit above that is split 50/50." Above what? The "equity" in what: the property or the profit. How are the two apparently competing rights to be conjoined? This is why people hire lawyers: to make sure that the words clearly delineate what the mutual intention of the parties is. In contract negotiation, there is something called a "red line," which shows where the different drafts of a contract alter. I used to read the redline very, very carefully, word by word, to make sure that it seemed to capture the intent of what I thought had been the most recent agreement. If it did, I would then reread the entire contract, phrase by phrase, clause by clause, to make sure that a judge reading it could not help but understand it as I believed it was intended to be read as a whole. Drafting contracts is a painstaking business of understanding English prose. Here is ONE interpretation of the incoherent mess that you have provided. The intention may well have been that, if there was a profit, each partner would share 50-50 in that profit after each received back his or her FINAL NET investment. (I am not sure that was what was intended. Possibly only God knew whether these parties even reached a meeting of the minds, and no contract is valid unless there is reasonably demonstrable evidence of a meeting of the minds. God, however, is almost never deposed as a witness; service of process is exceedingly difficult.) If that was the intended meaning, initially the capitalization was $$\displaystyle x + 40 + x = = 275 \implies 2x = 235 \implies x = 117.5.$$ The man contributes 117.5 + 40 = 157.5, and the woman contributes 117.5, for a total of $$\displaystyle 157.5 + 117.5 = 275.0 \ \checkmark.$$ However, after the second transaction, the respective capitalizations are: $$\displaystyle 157.5 - 75 = 82.5 \text { and } 117.5 + 75 = 192.5.$$ Let's check. $$\displaystyle 82.5 + 192.5 = 275.0 \ \checkmark .$$ Now assuming we are guessing correctly what was intended by the ignorant fool of an academic who wrote this exercise, the proceeds are divided 192.5+25=217.5 to the woman, representing half the profit plus what she eventually contributed to the joint investment, and 82.5 + 25 = 107.5 to the man. Profits of 50 are divided equally, 25 to each. The principal is fully distributed based on the final investments of each party: 217.5+107.5= 325.0. That is a commercially reasonable answer in equity given the gobbldy gook you provided. Whether the academic who wrote the exercise intended that as an answer is of course unknowable. You might as well consult a Ouija board. #### Jomo ##### Elite Member In your initial post you said that the woman loaned the man 75k and then in a latter post that number became 70k. Which is it? In my post above I used 70k. You can modify my post to reflect the 75k value. #### mnnn ##### New member There is 90k in equity. The first 40k goes back to the man. This leaves 50k left over. The man gets 25k and the woman gets 25k. So the man gets 40k+25k = 65k and the woman gets 25k. This seems correct as 65k + 25k = 90k. Now the man still owes the woman$70k. So the woman needs to get back 25k + 70k = 95k. This means that all 90k from the equity goes to the woman and the man still owes the woman 5k

You just can't take the 70k out of the pot and give it to the woman as half of that money was hers anyways! Do you see that?

There is no reason, as I detailed above, to involve the 70k loan in the transaction for the house. It had nothing to do with the house other than the promise to pay it back after the house was sold. On the other hand that initial downpayment from the man had everything to do with the house. If you prefer you can think of the man loaning the woman 20k (so now they each put down 20k each on the house) and again this 20k loan to the woman has nothing to do with the house.

If you consider both loans independent with the purchase of the house, then the man loaned the woman 20k and the woman loaned the man 70k so in the end the woman loaned the man 50k.

After the sale of the house they each get back 45k. Then the man needs to pay the woman the 50k loan back.
There is 90k in equity.
The first 40k goes back to the man.
This leaves 50k left over.
The man gets 25k and the woman gets 25k.

So the man gets 40k+25k = 65k and the woman gets 25k. This seems correct as 65k + 25k = 90k.

Now the man still owes the woman \$70k. So the woman needs to get back 25k + 70k = 95k. This means that all 90k from the equity goes to the woman and the man still owes the woman 5k

You just can't take the 70k out of the pot and give it to the woman as half of that money was hers anyways! Do you see that?

There is no reason, as I detailed above, to involve the 70k loan in the transaction for the house. It had nothing to do with the house other than the promise to pay it back after the house was sold. On the other hand that initial downpayment from the man had everything to do with the house. If you prefer you can think of the man loaning the woman 20k (so now they each put down 20k each on the house) and again this 20k loan to the woman has nothing to do with the house.

If you consider both loans independent with the purchase of the house, then the man loaned the woman 20k and the woman loaned the man 70k so in the end the woman loaned the man 50k.

After the sale of the house they each get back 45k. Then the man needs to pay the woman the 50k loan back.
Hi Jomo,

I cannot thank you enough for not only engaging with me on this query but furthermore giving me such a patient and succinct response. I am incredibly grateful to you.

Best wishes,

Nikki
UK